1. an IMAP server: This will interface the Linux mailboxes with the webmail program. There are webmail apps that will hook directly into the mailboxes, but I tend to trust IMAP servers more. If you have an mbox setup, use UW-IMAP. For Maildir, use Courier-IMAP. Cyrus-IMAP is the best if you have a large expected user base.

2. A webmail program. THere is a plethora of them. I prefer Squirrelmail because it only requires PHP (IMAP extension not neccesary). If you do have the imap extensions available with PHP, Horde's IMP is very good as well.